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Article Dans Une Revue Journal of modern dynamics Année : 2007

On the cohomological equation for nilflows

Livio Flaminio
Giovanni Forni
  • Fonction : Auteur

Résumé

Let X be a vector field on a compact connected manifold M. An important question in dynamical systems is to know when a function g:M -> R is a coboundary for the flow generated by X, i.e. when there exists a function f: M->R such that Xf=g. In this article we investigate this question for nilflows on nilmanifolds. We show that there exists countably many independent Schwartz distributions D_n such that any sufficiently smooth function g is a coboundary iff it belongs to the kernel of all the distributions D_n.

Dates et versions

hal-00805429 , version 1 (27-03-2013)

Identifiants

Citer

Livio Flaminio, Giovanni Forni. On the cohomological equation for nilflows. Journal of modern dynamics, 2007, pp.Pages: 37 - 60, Issue 1, January 2007. ⟨10.3934/jmd.2007.1.37⟩. ⟨hal-00805429⟩
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